The claim, due to be published in an analysis paper this week, suggests "real incomes" could rise by up to 4% after 30 years, equivalent to £5 billion in 2012, as part of the UK.
A briefing paper from the Treasury claims the estimate is based on international evidence of a "border effect" between countries, which it says extends to those with free trade agreements.
"The absence of a border maximises trade and labour migration, and keeps open broader economic and cultural links," the briefing paper suggests.
The analysis paper is expected to be launched by Chancellor George Osborne, who visits Aberdeen this week.
The paper is expected to highlight estimates that trade between then US and Canada is thought to be 44% lower than it could be because of the international border between them.
Scotland exported £36 billion worth of goods and services to the rest of the UK in 2011, and imported £49 billion worth, the Treasury says.
The analysis suggests that exports from an independent Scotland to the continuing UK could be over 80% lower after 30 years, in the event of independence.
It will also look at labour movement, concluding that people are more likely to move from Scotland to the rest of the UK than the example of Germany and Austria.
A Better Together spokesman said: "If we didn't already have the single UK market we would create it, so it makes absolutely no sense to put up barriers with businesses and customers in the rest of the UK.
"Being part of the UK allows Scottish businesses to thrive and provides greater opportunities than we would have if we went it alone. Why on earth would we want to put this at risk for the sake of Alex Salmond's obsession with independence?"
A spokeswoman for Deputy First Minister Nicola Sturgeon said Scots would not take kindly to being lectured by a "deeply unpopular" Tory Chancellor with claims that "ignore both the reality of a modern single market and the very real damage Westminster decisions have done to Scotland's economy."
She said a majority of people in Scotland want to see economic decisions taken in Scotland for Scotland.
Ms Sturgeon's spokeswoman said: "With household budgets expected to fall by £1800 in the next two years as part of the UK - and at least another four years of cuts to Scotland's budget - it is only a Yes vote in 2014 that can deliver real opportunities for Scotland.
"Westminster's economic policies have seen key industries close down, communities abandoned and generations of Scots let down whilst making the UK the fourth most unequal country in the developed world.
"The Tories are trying to take the people of Scotland for fools if they think families facing real hardship will buy fantasy promises from George Osborne.
"As an independent country, in a single market not just with the rest of the UK but with the European Union - a position threatened by Westminster - we will finally be able to make our own decisions, to support our key industries, our workforce and to counteract the economic imbalance caused by London-based economic policy."